A two-wheeled motor vehicle equipped with a rear cushion for which damping force characteristics can be adjusted is conventionally known, and there is an arrangement in which a sub-tank, which is a separate body from a damper cylinder, is supported on a linking pipe linking a pair of left and right center pipes forming part of a vehicle body frame, and an adjustment mechanism for adjustment of damping force is attached to the sub-tank (ref. Patent Document 1) or an adjustment mechanism, which is a separate body from a damper cylinder, is mounted on a pillion step holder so as to be spaced from the damper cylinder (ref. Patent Document 2).